I somehow doubt that it will involve much actual science, and more fancy computer visuals with no meaning.

Martial arts, well its all mechanics really. Unless you start going into ki theory.

Important to the science of the throws used in jiu-jitsu is the idea of the centre of mass, theirs axis and the effects of applied torque (specificall how torque applied off-axis makes things rotate).

Strikes are vector addition of forces coming from rotation of joints (eg.the tangential force cause by hip rotation) and longtitudinal motion. Also included is conservation of energy and momentum, the effects of collisions and how elastic you can approximate them (the lost kinetic energy goes mostly into the other guys face!). And of course pressure exerted and stress/strain measurements.

Biomechanics is of huge importance to as is anatomy, particiularly muscles structure nerve endings and the freedom of movement for joints.

Since the spectrum is so broad at this point, the first thing I would ask is what do you want to do to set yourself apart from the hundreds of other shows that have done this approach? I'll tell you that the best thing you could do is to find your show a REPUTABLE and knowledgable scientific advisor. If you truly are interested in the scientific aspects of combatives and ESPECIALLY martial arts, you're going to need someone to bounce stuff off of to ensure the scientific integrity of your program. There are thousands of charlatains and people who don't know what they are spouting (basically telling lies). If you do one thing, don't be a sounding board for those people. If there is something that can not be proven or duplicated through a scientific method, it's bunk (ref. George Dillman).

I saw an article on BBC online about a Kung Fu school somewhere in London I think, that had a supposed physics student taking lessons and trying to explain what she was doing. It was what you should strive to not be. The story and associated web site were just plain bad. I'll see if I can't dig up the links.
EDIT: Here is the website I mentioned: http://www.kungfuscience.org/access.asp" [Broken]

Looking at the kung fu science thing another thing I'd mention is not to get too precoccuopied with breaking boards. To quote Bruce Lee:

"Boards don't hit back"

In the end a punch is supposed to hurt a person by damaging his skin, muscle and other tissues. Remember that, some biologists and bio-engineers might be able to tell you about the various strain responses of human flesh.

As for missiles etc, Try talking to military research organisations like Qinetiq, DSTL and MBDA. They won't be able to tell you any specifics because of the security involved in their work, but they might be able to tell you something more general.